Approximation for Convenience Yield with Mean-Reverting Commodity Price

Qiang Zhao,Guiding Gu

doi:10.4236/jmf.2015.53021

Qiang Zhao, Guiding Gu

Open Access

https://doi.org/10.4236/jmf.2015.53021

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Abstract

The convenience yield of commodities is an important factor influencing futures prices and its accurate measure is a hot issue. Standard option-based measures assume the commodity prices follow a geometric Brownian motion, while some empirical evidence supports that the commodity prices show mean-reverting properties. Using a mean-reverting price process, we derive an analytical convenience yield approximation. We use the soybean meal and strong wheat futures to compare the new measure with the existing approximations. Empirical study shows that the new method with the mean-reverting price process is a better approximation for convenience yields.

Highlights

Convenience yield measures the benefit from holding physical commodities that are not available from holding futures contracts
In the theory of storage as described in Kaldor (1939) [1] and Brennan (1958) [2], the futures price is considered to be the sum of spot price and the cost of storing and minus the benefit from owning the commodities, which is defined as the convenience yield
The results show that the storage costs are the main factor influencing the convenience yields of strong wheat futures, while the length of period effect is the main factor influencing the convenience yields of soybean meal futures

Summary

Introduction

Convenience yield measures the benefit from holding physical commodities that are not available from holding futures contracts. The economic institution is that instead of holding a long future contract, a holder of an inventory has the option to sell the commodity at any time before maturity if the spot price is high enough and if it does happen, he can buy the commodity back at a relatively low price when maturity The value of this strategy can be derived using no-arbitrage principles. Heaney (2002) [4] uses the analysis of Longstaff (1995) [3] to approximate the convenience yield as the difference between two floating-strike look-back options written on the underlying commodity and the futures contract He assumes that the investor has the perfect foresight of the price dynamics before maturity.

Traditional Approach

Convenience Yield Modeling Via Look-Back Options

Convenience Yield Modeling Via Asian Options

Convenience Yield Modeling Via Asian Options with Mean-Reverting Price

Empirical Analysis

Concluding Remarks